I read something about if it's mental fatigue perhaps it would increase the time for your REM stages more than your deep sleep stages, which would increase your time for dreams and consequently give you more opportunities of realizing it's a dream. On the other hand if it's physical tiredness, your deep sleep stages would last longer in order to repair your body, which would decrease you REM periods and would reduce somehow your possibilities, although I know there's people who is able to become lucid during those blurry dreams that seem to happen during deep sleep stages. I don't know. Usually when I'm physically exhausted, it's very hard for me to have a good recall because of I cannot easily wake up to take notes after waking up from a dream, and if I got to wake up, sometimes it's unreadable what I put on the paper . Sometimes I wake up knowing I was lucid last night but I barely remember something about it, if it's not just the feeling of me being lucid. Anyway, the most important thing, in my opinion, is your motivation for becoming lucid and something to help you wake up to take notes if you're writing a journal.